document.write( "Question 1060155: Find all zeros of f(x)=x^3-x^2+x-21 and write a complete linear factorization of f (x) \n" ); document.write( "

Algebra.Com's Answer #675180 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "Find all zeros of f(x)=x^3-x^2+x-21 and write a complete linear factorization of f (x)
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document.write( "One root is x= 3. You can check it directly.\r\n" );
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document.write( "It means that (x-3) is the factor of the polynomial which divides the polynomial without a remainder (\"The Remainder Theorem\").\r\n" );
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document.write( "So, make a long division and find the quotient .\r\n" );
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document.write( "It is a quadratic polynomial.\r\n" );
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document.write( "Check it discriminant to determine if this quadratic has real roots.\r\n" );
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\n" ); document.write( "\n" ); document.write( "From Wikipedia (https://en.wikipedia.org/wiki/Polynomial_remainder_theorem): \r
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document.write( "     The polynomial remainder theorem states that the remainder of the division of a polynomial f(x) by a linear polynomial  x-a is equal to  f(a).      \r\n" );
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document.write( "     In particular,  x-a is a divisor of  f(x) if and only if f(a)=0.\r\n" );
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